A device for initiating and/or promoting chemical and/or physical high-pressure reactions on samples by the action of microwaves is known from DE 41 14 525. The device shown therein has a cooling device in the upper region, therefore above the region in which the sample is arranged in the sample vessel, such that corresponding gaseous products that occur in the reaction chamber condense and can be fed back to the reaction. In order to lock the coupling opening securely, relatively high temperatures are desired in a region of the sample vessel which surrounds the sample itself, such that said region can expand in a corresponding fashion in order to come into full abutment with the high-pressure vessel. The cooling in a region of the high-pressure vessel and the relatively high heating in another region of the high-pressure vessel result, on the one hand, in high tensions in the material of the high-pressure vessel. On the other hand, in particular in the highly heated region of the high-pressure vessel, the latter is, owing to the high thermal changes in each sample run, so highly stressed that its operating life is limited.